To solve the inequality \(-30 + 5x \leq 4(8x + 6)\), we start by distributing on the right side:
\[ 4(8x + 6) = 32x + 24 \]
Now, we can rewrite the inequality:
\[ -30 + 5x \leq 32x + 24 \]
Next, let's get all terms involving \(x\) on one side and constant terms on the other side. We can do this by subtracting \(5x\) and \(24\) from both sides:
\[ -30 - 24 \leq 32x - 5x \]
This simplifies to:
\[ -54 \leq 27x \]
Now, divide both sides by \(27\):
\[ -\frac{54}{27} \leq x \]
This simplifies to:
\[ -2 \leq x \]
or, alternatively:
\[ x \geq -2 \]
Thus, the solution to the inequality is:
\[ x \geq -2 \]
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